Let \(P\) be a closed subgroup of a Lie group \(G\) such that \(G/P\) is connected and the action of \(G\) on \(G/P\) is faithful. Suppose that \(\mathcal F\) is a \((G,G/P)\)-foliation on a compact, connected manifold with holonomy group \(\Gamma\). If \(\overline\Gamma\) is connected then either all holonomy covers of the leaves of \(\mathcal F\) have polynomial growth with a common bounded degree or they all have exponential growth. Links to examples of transversely projective foliations, i.e., \((\text{PSL}(2;\mathbb R),\mathbb RP^1)\)-foliations, are given.